Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general. Read more...
Preface
Contents
Chapter I Conformal Symmetry and Fields
I.1 Conformal Invariance
I.2 Symmetries and currents
I.3 Operator product expansion
I.4 Central charge and Virasoro algebra
I.5 Free bosons and fermions on a plane
I.6 Conformed ghost systems
Chapter II Representations of the Virasoro Algebra
II. 1 Fields and states
II. 2 Correlation functions
II. 3 Conformal bootstrap
II. 4 Null states
II. 5 Fusion rules
II. 6 Coulomb gas picture
II. 7 Ising and other statistical models
II. 8 Operator algebra and bootstrap in the minimal models
II. 9 Felder's (BRST) approach to minimal models. Chapter III Partition Functions and BosonizationIII. 1 Free fermions on a torus
III. 2 Free bosons on a torus
III. 3 Chiral bosonization
III. 4 Chiral bosonization on Riemann surfaces
III. 5 BRST approach to minimal models on a torus
Chapter IV AKM Algebras and WZNW Theories
IV. 1 AKM algebras and their representations
IV. 2 Sugawara-Sommerfeld construction
IV. 3 WZNW theories
IV. 4 Free field AKM representations
IV. 5 AKM characters, and the A-D-E classification of modular invariant partition functions
Chapter V Superconformal and Super-AKM Symmetries. V.1 Superconformal algebras and their unitary representationsV. 2 Super-AKM algebra and its representations
V.3 Supersymmetric WZNW theories
V.4 Chiral rings and Landau-Ginzburg models
Chapter VI Coset Models
VI. 1 Goddard-Kent-Olive construction
VI. 2 Kazama-Suzuki construction
VI. 3 KS construction and LG models
VI. 4 Gauged WZNW theories
VI. 5 Felder's (BRST) approach to coset models
VI. 6 Generalized affine-Virasoro construction
Chapter VII W Algebras
VII. 1 W3 algebra and its generalizations
VII. 2 Free field approach
VII. 3 Quantum Drinfeld-Sokolov reduction. VII.4 W coset constructionChapter VIII Conformal Field Theory and Strings
VIII.1 Bosonic strings in D d"26
VIII.2 Supersymmetry and picture-changing
VIII.3 Extended fermionic strings
VIII.4 W gravity and W strings
Chapter IX Quantum 2d Gravity, and Topological Field Theories
IX.1 Quantum 2d gravity
IX.2 Liouville theory
IX.3 Topological field theories and strings
Chapter X CFT and Matrix Models
X.1 Why matrix models?
X.2 One-matrix model solution
X.3 Multi-matrix models
X.4 Matrix models and KdV
Chapter XI CFT and Integrable Models
XI.1 KdV-type hierarchies and flows. XI. 2 W-flowsXI. 3 WZNW models and Toda field theories
XI. 4 4d self-duality and 2d integrable models
XI. 5 Self-duality and supersymmetry
Chapter XII Comments
XII. 1 About the Literature
XII. 2 Basic facts about Lie and AKM algebras
XII. 3 Basic facts about V-functions
XII. 4 Basic facts about Riemann surfaces
XII. 5 Basic Facts about BRST and BFV
XII. 6 CFT and quantum groups
Bibliography
Text Abbreviations
Index.
